Probing the scalar-induced gravitational waves with the Five-hundred-meter Aperture Spherical radio Telescope and the Square Kilometer Array*

Gravitational-wave astronomy offers a promising opportunity to directly observe scalar-induced gravitational waves originating from the early universe. Experiments—including ground-based interferometers such as LIGO and Virgo, and pulsar timing arrays (PTAs) based on facilities such as FAST and SKA—are poised to significantly enhance sensitivity to these signals. In this paper, we combine Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillation (BAO) datasets with upper or lower limits on the stochastic gravitational-wave background provided by FAST or SKA to constrain scalar-induced gravitational waves. To provide a comprehensive forecast, we consider two scenarios at a given frequency: one in which FAST or SKA does not detect scalar-induced gravitational waves, thereby setting an upper limit on the fractional energy density; and another in which these waves are detected, thus establishing a lower limit. In the ΛCDM+ r model, the scalar spectral index of the power-law power spectrum is constrained to from the combination of CMB+BAO+SKA datasets in the upper-limit scenario where scalar-induced gravitational waves propagate at the speed of light. The constraint shifts to in the lower-limit scenario. Compared with the constraint from the combination of CMB+BAO datasets, the scalar spectral index in the upper-limit scenario exhibits significant changes, which could serve as an indicator of scalar-induced gravitational waves. In the ΛCDM+ + r and ΛCDM+ + + r models, the running of the scalar spectral index and the running of the running also show notable variations, suggesting potential indicators. The numerical findings clearly demonstrate the impact of the upper and lower limits provided by FAST or SKA.